To fully understand this phrasing, let's look at this entire section of text:
The witnesses for the state, with the exception of the sheriff of Maycomb County, have presented themselves to you gentlemen, to this court, in the cynical confidence that their testimony would not be doubted, confident that you gentlemen would go along with them on the assumption—the evil assumption—that all Negroes lie, that all Negroes are basically immoral beings, that all Negro men are not to be trusted around our women, an assumption one associates with minds of their caliber.
The "witnesses of the state" whom Atticus is primarily focused on are Bob and Mayella Ewell. Bob presents himself as a profane and ignorant man, and Mayella offers testimony that is argumentative and fearful. It is clear that neither of the Ewells are telling the truth and are instead depending on an all-white jury to convict Tom simply because his accusers are white.
In this quote, it's first important to define "caliber." A good synonym would be ability. Atticus is therefore saying that assuming that all Black people lie, are immoral, and cannot be trusted around women is a mindset that people associate with minds of "their" abilities.
Next, it's important to define who "they" are. If we go back to the beginning of this quote, we find the original subject: the witnesses for the state. Thus, Atticus's point is that these racist beliefs are commonly associated with people like Bob and Mayella Ewell, who have low-ability minds. In essence, he equates racist attitudes with being unintelligent.
This is a convincing persuasive technique; he is asking the jury to prove themselves different from the Ewells, who are not respected in Maycomb, by refusing to accept these common stereotypes. Unfortunately, the jury fails to listen to Atticus's pleas.